Galois Groups and Fundamental Groups

by Edited by Leila Schneps

• ISBN13: 9780521808316
• ISBN10: 0521808316
• Format: Hardcover
• Copyright: 2003-07-21
• Publisher: Cambridge University Press

Summary

This book contains eight expository articles by well-known authors of the theory of Galois groups and fundamental groups. They focus on presenting recent developments, avoiding classical aspects which have already been described at length in the standard literature. The volume grew from the special semester held at the MSRI in Berkeley in 1999 and many of the new results are due to work accomplished during that program. Among the subjects covered are elliptic surfaces, Grothendieck's anabelian conjecture, fundamental groups of curves and differential Galois theory in positive characteristic. Although the articles contain original results, the authors have striven to make them as introductory as possible, making them accessible to graduate students as well as researchers in algebraic geometry and number theory. The volume also contains a lengthy overview by Leila Schneps that sets the individual articles into the broader context of contemporary research in Galois groups.

Table of Contents

1. Monodromy of elliptic surfaces

2. Topics surrounding the anabelian geometry of hyperbolic curve

3. Tannakian fundamental groups associated to Galois groups

4. Automorphisms of curves and special loci in genus zero moduli spaces

5. On the tame fundamental groups of curves over algebraically closed fields of characteristic 0

6. Constructive differential Galois theory

7. Monodromy groups of coverings of curves

8. On the specialization homomorphism of fundamental groups of curves in positive characteristic.